Module 5: Function Concept - Functions and Non-Functions
This module uses a Vending Machine GeoGebra applet designed to support students’ understanding of the concept of function. Video clips of students’ work with the applet and their resulting proposed definitions of function provide the context in which teachers will notice and predict student thinking, as well as select, sequence, and connect student work. Finally, teachers will consider how to use this work along with the technology to facilitate the development of the definition of function.
There are two versions of some of the activities in this module. They are the same except they use different versions of the Vending Machine applet. Those labeled with an “R” use a version designed for students revisiting the concept of function and those labeled with an “I” use a version designed to introduce the concept of function.
This module could be used alongside a Chapter from Teaching Algebra materials:
Chapter 6: Functions.
For more details see the Module Overview document.
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Module Elements
5.1 Vending Machine Task (Revisiting the Concept of Function Version)
Teachers engage individually with the Vending Machine applet. As they work through the applet, they complete a written worksheet that has them classify each machine as either function or non-function and describe how they know.
Class Materials
5.2 Noticing Student Thinking: Machine G of the Vending Machine Task
Teachers examine video clips of multiple pairs of students engaging with a specific machine, G, and are tasked with focusing on how the students’ interactions with the Vending Machine applet lead them to their determination of function/non-function.5.3 Noticing and Predicting: The Vending Machine Task
Teachers attend and interpret students’ understanding of function and engagement with the Vending Machine applet. Teachers are then asked to predict how the students will respond to the following vending machines based on their analysis.*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.
5.4 Selecting and Sequencing: Defining Function with the Vending Machine Task
Teachers are given 20 student created definitions, asked to select 4-5, sequence them and discuss connections they would make during a whole class discussion.
*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.
5.5 Anticipating Student Thinking: Concept Images of Function and the Vending Machine Task
Teachers will consider how students’ concept images of function led to their classification of Vending machines as functions or non-functions. Teachers are asked to consider how anticipating students’ concept images can help inform their practice.5.6 Orchestrating Whole Class Discussions: Defining Function with the Vending Machine Task
Teachers are presented with the first few lines of a whole class discussion that would follow students engaging with the Vending Machine applet and creating their own definitions of function. They are asked to script out the next 8 - 10 lines of the discussion and explain how their choices met the stated discussion goal.
*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.